随机波动率跳跃扩散模型下重置期权定价

发布时间：2018-02-09 16:27

本文关键词： 随机波动率跳跃扩散模型时点重置期权 Girsanov测度变换 Fourier反变换　出处：《广西师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：期权作为投资和风险管理的核心工具,一直以来倍受金融业界和学术界的重视,期权定价是研究金融衍生品的核心内容之一.随着期权及其相关理论的不断完善,衍生出各种新型奇异期权.在金融市场中,重置期权是交易最活跃的奇异期权,因此本文主要研究重置期权.重置期权是一种投资者可以重新设定期权执行价格的奇异期权,使投资者拥有比一般期权更多的权利和收益.重置期权分为时点重置期权和水平重置期权.本文主要结合时点重置期权进行研究.时点重置期权是一种在有效期内某些预先规定时点上重新设置期权执行价格的期权.时点重置期权大多是基于Black-Scholes模型,但Black-Scholes模型并不符合实际金融市场中金融资产的运动特征.因为真实的金融市场处于不稳定状态,会受到许多外部不确定信息流或突发事件的干扰导致市场急剧震荡,从而导致利率、波动率和股价的波动和跳跃.为了更好地刻画期权定价,金融学者们改进了 Black-Scholes模型,通过假设利率、波动率、股价为随机且跳跃的,建立了随机波动率跳跃扩散模型.随机波动率跳跃扩散模型优势在于期权波动率、利率、标的资产的变化服从离散跳跃过程和连续随机过程作用下的几何布朗运动.在该模型下研究时点重置期权定价非常必要.本文引入随机波动率跳跃扩散模型,对单资产重置期权和多资产几何平均下重置期权进行研究.首先通过证明利率和波动率都符合线性的仿射结构,建立跳跃扩散模型.然后得出期权及其波动率、利率的联合特征函数,运用Girsanov测度变换和Fourier反变换得到单资产重置期权的定价.为了减少投资者对时点重置期权操控,本文又将单资产重置期权应用推广到几何平均多资产重置期权上.最后通过数值,分析股价跳跃,波动率和利率对重置期权的影响.分析结果表明波动率跳跃强度λv、波动率跳跃相关系数ρJ、利率跳跃强度λr和利率跳跃相关系数ρr对单时点重置期权都有正影响,且单时点重置期权价格随相关系数的增大而增大.波动率跳跃相关系数ρJ和利率跳跃相关系数ρr对单时点重置期权的影响是平稳的,而波动率跳跃强度λv和利率跳跃强度λr对单时点重置期权的影响是先缓慢后加快.投资者利用单时点重置期进行套期保值过程中,不但关注平稳下的跳跃波动风险,而且要重视股价急剧动荡所带来的跳跃波动风险.
[Abstract]:As the core tool of investment and risk management, option pricing has been paid more and more attention by the financial industry and academic circles. Option pricing is one of the core contents of financial derivatives research. In the financial market, the replacement option is the most active singular option, so this paper mainly studies the replacement option, which is a kind of strange option that investors can set the executive price of the option. The replacement option is divided into time reset option and horizontal reset option. This paper mainly studies the time point replacement option, which is a kind of time point replacement option, which is a kind of time point replacement option. An option that resets the executive price of an option at certain predetermined points in time. The timepoint reset option is mostly based on the Black-Scholes model. However, the Black-Scholes model does not accord with the characteristics of financial assets movement in the actual financial market. Because the real financial market is in an unstable state, it will be disturbed by a lot of external uncertain information flows or unexpected events, which will lead to sharp market shocks. In order to better characterize option pricing, financial scholars have improved the Black-Scholes model by assuming that interest rates, volatility, and stock prices are random and jump. A stochastic volatility jump diffusion model is established. The advantage of stochastic volatility jump diffusion model lies in option volatility, interest rate, The change of underlying assets is governed by geometric Brownian motion under the action of discrete jump process and continuous stochastic process. It is necessary to study the pricing of time replacement option in this model. In this paper, a stochastic volatility jump diffusion model is introduced. The single asset replacement option and the multiple asset geometric average replacement option are studied. Firstly, the jump diffusion model is established by proving that both interest rate and volatility conform to the linear affine structure, and then the options and their volatility are obtained. The joint characteristic function of interest rate, using Girsanov measure transform and Fourier inverse transform to get the pricing of single asset replacement option. In this paper, the application of single asset replacement option is extended to geometric average multiple asset replacement options. The results show that volatility jump intensity 位 v, volatility jump correlation coefficient 蟻 J, interest rate jump intensity 位 r and interest rate jump correlation coefficient 蟻 r have positive effects on single time replacement option. Moreover, the price of single-point replacement option increases with the increase of correlation coefficient. The effect of volatility jump correlation coefficient 蟻 J and interest rate jump correlation coefficient 蟻 r on single-time replacement option is stable. However, the impact of volatility jump intensity 位 v and interest rate jump intensity 位 r on single time replacement option is slow and then accelerated. Investors not only pay attention to the jump volatility risk in the process of hedging with single time point replacement period, but also pay attention to the jump volatility risk under stationary condition. And should pay attention to the sharp volatility of stock prices brought about by the risk of jumping volatility.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F830.9

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